Let's share ridiculous ideas for how to implement the theme!

I've grouped these by general reason as to why you can't, or (probably?) won't, play it again.

The Game Is Radically Different Each Time, So You Can Never Play "The Same" Game Twice

• The nature of the game is inextricably tied to the exact real-world date and the time you play it.
• The game changes every time it is played, so it's very different if this is the fifth time for at least one player than it is for the first.
• The process of playing the game changes the rules.

The Game Contains A Secret, And Is Unplayable Once You Know It

• The game is about working out what the rules actually are.
• You play pre-set characters with amnesia. The game is about discovering who you are.

The Game Never Ends

• The game specifically prohibits stopping playing it. The only way to stop is to break the rules.
• The game slides invisibly into your regular life, forever, perhaps awarding you points as you go or something.
• I just lost the Game, by the way.

The Game Text Is Destroyed

• It's written in photosensitive ink, that fades as you read it.
• As you play, you tear out pages of the rules.
• There's a supplementary material (an audio or video tape, perhaps) which self-destructs at the end.

The Players Are Destroyed

• The game involves revealing secrets about yourselves, giving voice to all your innermost thoughts. The game ends only once people are sufficiently distrubed to no logner want to be your friends.
• As you play, you burn your possessions. The game ends when you are naked, homeless and destitute.
• The game sends you incurably insane by the end.
• The game ends with the deaths of one or more players.

The Play Space Is Destroyed

• The game culminates with the end of the universe. The actual universe.
• Begin play by turning on all the taps in the building and plugging up all drains. When the play area is flooded and is no longer habitable, the game is over.

May I add:

The Game Must be Played Under Specific, Non-Repeatable Circumstances

• The game is meant as a "final game" when members of a group move away.
• All players must be smokers, and the game ends when all have quit.
• The game begins at 12:00 AM GMT, December 12, 2012 and ends 24 hours later.

The Game is So Terrible, Nobody Would Ever Want to Play It Again

• The rules are patently senseless and incomplete.
• The entire document is abysmally formatted and offensive.
• Like, 90% of the time you die during character generation.

The game includes clues to a real life treasure and the goal of the game is to decode the puzzles and find the real world treasure.

Adding to:

The Play Space Is Destroyed

• A candle is lit, the gas is turned on.  The game ends when the play space explodes.

New:

The Game Materials are Destroyed

• The dice are smashed when rolled.  The pieces are then cast as scrying stones.  Then smashed again.
• The cards are burned when selected.  The players heap the ash in a pile in front of them.  The ash represents their dead ancestors.
• Instead of being rolled, the dice are swallowed.  Any numbers not worn off by digestive acids are counted as the outcome of the roll.

The game is made to enact real world changes.  Once those changes have been completed, repeated playthroughs would be pointless.  For example (relevant to the four word ingredients), getting an individual or individual covertly across a border, curing a disease.

I did this: The game is about working out what the rules actually are.
And this: The game specifically prohibits stopping playing it. The only way to stop is to break the rules.
In a game I wrote called Reality. But I can't use that. Sadly someone already thought of Russian Roulette too, so that's out.
So now I'll just do this: The game culminates with the end of the universe. The actual universe.

Ideas:
The game takes a lifetime to play.
You play the game when you turn a certain age. Perfect for a mid life crisis game.

I'm working on a game with puzzle aspects... once the premise of the game is understood players are empowered to stop playing. The sooner they decide to , the "better" then ending.

The problem is.. play testing that experience is going to be intensive needing lots of people, and I'm not sure I want to invest a ton of time making a game I can't even play with my friends more than once.

The game is tied to real life time or date.
-The game is about the supposed 2012 apocalypse.  If it happens, then you can't play (because everyone is dead).  If it doesn't happen, you can't play (because the apocalypse has passed). 
-The game uses the date and time in the mechanical resolution, and esults past a certain point lead to divide by zero errors.
-The game is a birthday present for someone and will be played on their birthday and that day alone.

A game to be played during your own wake.  Pray that the game won't be playtested soon.

There is only one (not reproducible) copy of the game in the world, and you have to give it away after one game.

The game must be played by everybody at a precise date and time, that is so tied to the game that can't be postponed or changed.

The game is tied to something you have to do for the first time in your  life (your first date, your first kiss, your first sex, the birth of your first child, your first divorce, your first fistfight, etc.)

Moreno wrote:
There is only one (not reproducible) copy of the game in the world, and you have to give it away after one game.

mrteapot wrote:

Moreno wrote:
There is only one (not reproducible) copy of the game in the world, and you have to give it away after one game.

This seems gimmicky to me (why can't you make additional copies?).